Weight distribution of Preparata codes over Z_4 and the construction of 3-designs  

作　　者：LI WeiXia SHEN Hao 

机构地区：[1]School of Mathematical Sciences,Qingdao University [2]Department of Mathematics,Shanghai Jiao Tong University

出　　处：《Science China Mathematics》2014年第6期1155-1162,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11071163);Doctor Fund of Shandong Province(Grant No.BS2009SF017)

摘　　要：In this paper,we calculate the number of the codewords(with Hamming weight 7)of each type in the Preparata codes over Z4,then give the parameter sets of 3-designs constructed from the supports of the codewords of each type.Moreover,we prove that the first two families of 3-designs are simple and the third family of the 3-designs has repeated blocks.In this paper, we calculate the number of the codewords （with Hamming weight 7） of each type in the Preparata codes over Z4, then give the parameter sets of 3-designs constructed from the supports of the codewords of each type. Moreover, we prove that the first two families of 3-designs are simple and the third family of the 3-designs has repeated blocks.

关 键 词：T-DESIGNS weight distribution Preparata codes over Z4 

分 类 号：O157.4[理学—数学]